The present invention relates generally to data systems such as, for example, data storage systems, data communication systems, etc. More particularly, the present invention pertains to symbol detection techniques for use in such systems.
Data communication systems and data storage systems, e.g., digital versatile disk (DVD) systems, generally require application of signal processing techniques for operation. For example, symbol detection may be required to be applied to a channel of a system for determination of a symbol decision, e.g., a binary symbol decision. With respect to data storage systems, a dramatic increase in data storage density has come from improvements in system hardware, such as read heads, storage media, and also in the interface therebetween. However, increases in data storage can also be attributed to advances in signal processing.
For example, at high densities, readback signals suffer severely from bit crowding or inter-symbol interference (ISI) and also have very poor signal-to-noise ratio (SNR). Conventional readback processing, such as that which involves run-length limited (RLL) codes with peak detection and some readback equalization, is becoming inadequate at very high densities.
Various symbol detection techniques have been described for use in reducing the effects of ISI and for SNR to provide more reliable symbol detection. Generally, the symbol detection techniques can be classified as either maximum likelihood (ML) or decision feedback detectors. Typical of the former is the partial response (PR) maximum likelihood detector, and typical of the latter is the fixed delay tree search with decision feedback (FDTS/DF) detector (e.g., which has been used for symbol detection in DVD channels).
One particular symbol detection technique referred to as signal-space detection has gained attention. For example, as described in an article entitled, “Delay-Constrained Asymptotically Optimal Detection using Signal-Space Partitioning,” by Younggyun Kim and Jaekyun Moon, ICC '98-1998 IEEE International Conference On Communications (June 1998), an illustrative signal-space detector may estimate a channel input signal based on the location of a finite length observation signal in a multidimensional signal-space. The decision boundary is formed by a set of hyperplanes.
For example, as described therein, a discrete time channel model can be represented by:
      r    k    =                    ∑                  i          =          0                L            ⁢                        f          i                ⁢                  a                      k            -            i                                +          n      k      where rk is an observation sample, {fl} represents the overall channel response (f0≠0), ak is the input symbol taken from {+1, −1}, and nk is additive white Gaussian noise. A signal-space detector with a decision delay of τ makes a decision on symbol ak−l at time k based on observation samples {rk−l}, 0 ≦i≦τ. Past decisions on the input symbols {ak−l},i>τ, are used to cancel ISI terms from observation samples. In this process, past decisions are assumed to be correct. After canceling ISI terms, the detector has the observation samples represented by:
            x              k        -        j              =                                        ∑                          i              =              0                                      τ              -              j                                ⁢                                    f              i                        ⁢                          a                              k                -                j                -                i                                                    +                  n                      k            -            j                              =                        s                      k            -            j                          +                  n                      k            -            j                                ,          ⁢      0    ≤    j    ≤    τ  where sk−j is the noiseless signal. The detector finds the most probable noiseless signal vector s=[sk, . . . , sk−τ]T based on the observation sample vector x=[xk, . . . , xk−τ]T and releases the symbol decision on ak−τ, which is consistent with the most probable signal vector. This can be viewed as partitioning the (τ+1)-dimensional observation space into two decision regions, where two regions are separated by a set of hyperplanes.
The complexity of this detector, as well as the others described above, are undesirable. Optimal performance in a linear channel with additive noise can be achieved by a maximum likelihood sequence detector (MLSD), which is efficiently implemented using a Viterbi algorithm. However, the complexity of such a detector in severe ISI environments makes it impractical for commercial storage applications. PR maximum likelihood offers a detector that is a compromise between complexity and performance by equalizing the channel to a shorter impulse response at the expense of increasing the noise power seen by the detector. Likewise, FDTS/DF detectors provide a trade-off between complexity and performance that can be varied by changing the delay length thereof. As delay length increases, the performance also increases. However, complexity increases along with it. As one might expect, it is desirable to reduce complexity yet retain performance required for desired particular applications.